具有隐私保护的分布式共轭对偶梯度算法  

Privacy-preserving Distributed Optimization Based on Conjugate Dual Gradient Methods

作　　者：吕净阁 李德权 LV Jingge;LI Dequan(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 23200)

机构地区：[1]安徽理工大学数学与大数据学院,淮南232000

出　　处：《长春理工大学学报（自然科学版）》2018年第3期120-125,134,共7页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：安徽省高校学科(专业)拔尖人才学术资助重点项目(gxbj ZD2016049)

摘　　要：针对多个体系统中个体(节点)间信息交流易导致隐私泄露的问题,提出了一种基于共轭对偶梯度(CDG)的隐私保护算法—隐私保护分布式共轭对偶梯度算法(PP-CDG)。首先,针对优化问题研究了共轭对偶梯度算法,通过添加正则项来防止共轭函数震荡、保证界更小、便于有效地进行对偶转换;其次,将同态加密机制(Paillier Cryptosystem)与共轭对偶梯度算法相结合提出PP-CDG算法,并证明当网络无向时变且本地损失函数是强凸时所提算法的收敛性;最后,进一步的理论分析表明敌对个体在收集多步中间信息时无法窃取邻居个体的敏感信息,因此算法能够有效保护个体的隐私。Aiming at the problem of privacy leakage caused by the direct exchange of information between agents in multi-agents systems, a privacy-preserving distributed optimization algorithm based on Conjugate Dual Gradient（CDG） —the Privacy-preserving Conjugate Dual Gradient（PP-CDG） algorithm is proposed. Firstly,the conjugate dual gradient algorithm is studied for the optimization problem by adding regular terms to the conjugate function in order to prevent the tendency to oscillate,together with the aim to guarantee an obtained smaller bounds and to facilitate the dual transformation efficiently. Secondly, a Privacy-preserving Conjugate Dual Gradient is proposed by combining the Paillier Cryptosystem mechanism with the conjugate dual gradient algorithm and its convergence is proved for the cases that the networks are undirected time-varying and the local loss functions are strongly convex. Finally, it is provesd that the adversaries agent cannot obtain the sensitive information of its neighbors even by the intentional collection of multi-step intermediate information through further theoretical analysis,and thus the proposed algorithm can effectively ensure the privacy protection of agents.

关 键 词：分布式优化 对偶梯度 同态加密技术 隐私保护 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]